Rhaego was the stillborn son of Daenerys Targaryen and Drogo. The reason for his stillbirth is that his mother asked a maegi in the village, Mirri Maz Duur, to save his father's life, as Drogo was dying of an infected wound). Mirri saves Drogo's life, but in payment she kills Rhaego while he is still in Daenerys's womb. Daenerys never sees her son but she is told that he was hideously deformed with scales of a dragon, and traces of wings.
While he may have been born deformed, this was only due to blood magic performed by Mirri Maz Duur. In the first book, A Game of Thrones, Daenerys has a vision of him with copper skin, platinum blonde hair, and almond-shaped violet eyes. This is most likely how he would have looked like, had he survived.
A Game of Thrones.
Rhaego is prophesied to be the stallion who mounts the world by the crones of the dosh khaleen at Vaes Dothrak just after the stallion heart ceremony.
After Rhaego's father, Drogo, becomes sick from an infected wound, the sorceress Mirri Maz Duur saves Drogo's life by using blood magic. One of the effects of that magic is that Rhaego dies right before birth. He was inhuman, hideously deformed and covered in dragon-like scales. He had the stub of a tail small leather wings, reminiscent of a bat. Rhaego was stillborn.
During her fever dream, Daenerys Targaryen sees her son tall and proud, with Drogo's copper skin and her own silver-gold hair, violet eyes shaped like almonds. He smiles at her and begins to lift his hand towards her, but when he opens his mouth fire pours out. She sees his heart burning through his chest and in an instant he is gone, consumed like a moth by a candle, turned to ash.